Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces

Multiple Solutions for Quasilinear Elliptic Neumann Problems in Orlicz-sobolev Spaces

Here, Ω is a bounded domain with sufficiently smooth (e.g. Lipschitz) boundary ∂Ω and ∂/∂ν denotes the (outward) normal derivative on ∂Ω. We assume that the function φ :R→R, defined by φ(s)= α(|s|)s if s = 0 and 0 otherwise, is an increasing homeomorphism from R to R. Let Φ(s)= ∫ s 0 φ(t)dt, s∈R. Then Φ is a Young function. We denote by LΦ the Orlicz space associated withΦ and by ‖ · ‖Φ the usu...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Orlicz Spaces and Nonlinear Elliptic Eigenvalue Problems

Nonlinear elliptic differential equations of order m acting in a space of m dimensions often occupy a special position in more general theories. In this paper we shall study one aspect of this situation. The nonlinear problem under consideration will be the variational approach to eigenvalue problems for nonlinear elliptic partial differential equations as developed by the author in [l], [2], [...

Dirichlet and Neumann Boundary Values of Solutions to Higher Order Elliptic Equations

We show that if u is a solution to a linear elliptic differential equation of order 2m ≥ 2 in the half-space with t-independent coefficients, and if u satisfies certain area integral estimates, then the Dirichlet and Neumann boundary values of u exist and lie in a Lebesgue space Lp(Rn) or Sobolev space Ẇ p ±1(R n). Even in the case where u is a solution to a second order equation, our results a...